Abstract: In the last chapter we discussed planar shock reflection and solve some corresponding problems by using shock polar. Generally the incident shock is not a planar shock, and the surface of the obstacle is not a plane. Then the method of shock polar can only give an approximate solution near the reflective point. In order to obtain the precise solution, people must use mathematical analysis based on the theory of partial differential equations, i.e. look for the solution to an assigned boundary value problem of a partial differential equation. In this chapter we will discuss the regular reflection of shock by a curved surface of an obstacle. The solutions under consideration are piecewise smooth ones, in which shock or other nonlinear waves are admissible. These solutions may have discontinuity on the front of nonlinear waves, while keep continuously differentiable elsewhere. The main references of this chapter are [1–3].